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TOF spectroscopy is well suited to experiments that involve surveying large ranges in either energy transfer or energy and momentum transfer space. Developments in both instrumentation and experimental techniques have opened up new scientific opportunities and produced some outstanding results to date. These developments show every sign of continuing, fuelled by the opportunities for constructing stateof- the-art instrumentation for the next generation sources currently under construction or in planning.

We have presented the Multiple Scattering Theory applied to the calculation of X-ray absorption spectra. We have specially outlined that in this technique the contributions from the potential and from the structure could be separated. The essence of the theory resides in solving equations of continuity that have a compact expression in the case of “muffin-tin” potentials. The construction of the potential has been developed with some emphasis concerning the exchange and correlation potential of common use for X-ray absorption calculations. The application of the Multiple Scattering Theory has been exemplified on a series of edges for divalent vanadium, iron and copper in solution. The influence of various parameters has been illustrated: formulations of the final state, influence of the bond distance, resonance of the phase shifts and local symmetry around the absorbing atom. A more complicated case has also been illustrated where the influence of spin conversion and coordination sphere contraction at iron edges could be separated through calculations in the MST framework.

The MST is still a very active field and many theoretical developments took place during the last seven years around Rino Natoli (X-ray Natural Circular Dichroism), John Rehr (the various FEFF codes), Dave Foulis (non “muffin-tin” code), Adriano Filipponi and Andrea di Cicco (coupling Molecular Dynamics and XANES calculations), Yves Joly (comparative approach of MST and Finite Differences Method), Christian Brouder (semi-relativistic approach) or Hubert Ebert (XMCD at and edges).

Photoelectron spectroscopy is probably the best practical realization of the theorist’s dream of probing the properties of a single particle in an interacting many-body system. Remarkably, although photoemission is certainly a “highenergy” spectroscopy, the large excitation energy does not destroy even subtle signatures of correlations. On the contrary, the close connection with the oneparticle Green’s function ensures that the spectrum carries momentum-resolved information at all the relevant energy scales, down to the low-lying excitations that shape the thermodynamic properties. It was the goal of this chapter to illustrate this simple but important idea, which is validated by recent experimental results both on model systems and on exciting new materials. This guideline, and the continuous improvements in experimental conditions, namely exploiting the unique properties of SR sources, holds promise for exciting future developments.

Over the last thirty years neutron spin echo spectroscopy has evolved from an ingenious concept to a powerful workhorse. Its many unique characteristics, including its wide dynamic range and ultra-high resolution, the ability to measure the intermediate scattering law directly, the simplicity of the resolution corrections, and the added advantage of polarization analysis of the scattering from the sample has ensured its position as an indispensable tool in studies of slow relaxation phenomena in all fields of condensed matter research. There is little doubt that the continually increasing sophistication of spin echo instrumentation will enable the effective implementation of powerful time-of-flight NSE techniques at the new high intensity third generation spallation sources now being built in the US and Japan, and being planned in Europe.

In this chapter, we have addressed the issues of an IR beam extracted from a synchrotron ring, and reported on its potentiality for the investigation of the vibrational properties of interfaces, especially in the far IR spectral range, where conventional sources are too low in brightness. Several FTIR instruments are operating or being developed on several synchrotron rings and are expected to bring valuable quantitative information on the adsorbate-substrate bonding, as well as their vibrational dynamics. Accessing this information should be a critical step towards a better understanding of the energetics and the kinetics of interfacial processes, especially in electrochemical interfaces, where adsorption is always a competitive process between the ionic species and the solvent dipoles, which is controlled by the electrode potential.

The development of optical non-linear techniques benefits directly from the progress of the laser technology. In this respect, the Free electron laser offers a great advantage of producing a high power pulsed beam, tunable within a wide IR spectral range, allowing the simultaneous probe of several vibrational modes of the adsorbate. Combining the unique properties of the FEL with the high sensitivity and interface selectivity of SFG between centro-symmetric media allows the investigation of the vibrational properties of adsorbate species, with no interference from a signal of bulk species, which is forbidden in the electric dipole approximation. The recent experimental examples discussed in this lecture show clearly the advantage of this technique. The use of SFG, as well as various related second order optical processes, is increasing rapidly in various surface and interface research fields such as catalysis, corrosion, electrocatalysis, thanks to its versatility, its capability to probe any interface.

Photoelectron spectroscopy is probably the best practical realization of the theorist’s dream of probing the properties of a single particle in an interacting many-body system. Remarkably, although photoemission is certainly a “highenergy” spectroscopy, the large excitation energy does not destroy even subtle signatures of correlations. On the contrary, the close connection with the oneparticle Green’s function ensures that the spectrum carries momentum-resolved information at all the relevant energy scales, down to the low-lying excitations that shape the thermodynamic properties. It was the goal of this chapter to illustrate this simple but important idea, which is validated by recent experimental results both on model systems and on exciting new materials. This guideline, and the continuous improvements in experimental conditions, namely exploiting the unique properties of SR sources, holds promise for exciting future developments.

Anomalous or resonant diffraction can be used to obtain much information about a given element in a crystal. However this information requires sophisticated tools (synchrotron rings), accurate experiments and complex analysis. This is a price that still needs to be paid to go beyond the anomalous complexity and/or correction and to fully extract and use this rich “” information. However, several applications are nowadays available for the MAD method to determine experimentally the phase and for the contrast method that uses the chemical sensitivity of resonant diffraction. This is also the case for the DAFS method: the fine structure of the diffracted intensity as a function of the energy can now be analyzed in very complex structures or systems.

Photoelectron spectroscopy is probably the best practical realization of the theorist’s dream of probing the properties of a single particle in an interacting many-body system. Remarkably, although photoemission is certainly a “highenergy” spectroscopy, the large excitation energy does not destroy even subtle signatures of correlations. On the contrary, the close connection with the oneparticle Green’s function ensures that the spectrum carries momentum-resolved information at all the relevant energy scales, down to the low-lying excitations that shape the thermodynamic properties. It was the goal of this chapter to illustrate this simple but important idea, which is validated by recent experimental results both on model systems and on exciting new materials. This guideline, and the continuous improvements in experimental conditions, namely exploiting the unique properties of SR sources, holds promise for exciting future developments.

Over the last thirty years neutron spin echo spectroscopy has evolved from an ingenious concept to a powerful workhorse. Its many unique characteristics, including its wide dynamic range and ultra-high resolution, the ability to measure the intermediate scattering law directly, the simplicity of the resolution corrections, and the added advantage of polarization analysis of the scattering from the sample has ensured its position as an indispensable tool in studies of slow relaxation phenomena in all fields of condensed matter research. There is little doubt that the continually increasing sophistication of spin echo instrumentation will enable the effective implementation of powerful time-of-flight NSE techniques at the new high intensity third generation spallation sources now being built in the US and Japan, and being planned in Europe.

In this chapter, we have addressed the issues of an IR beam extracted from a synchrotron ring, and reported on its potentiality for the investigation of the vibrational properties of interfaces, especially in the far IR spectral range, where conventional sources are too low in brightness. Several FTIR instruments are operating or being developed on several synchrotron rings and are expected to bring valuable quantitative information on the adsorbate-substrate bonding, as well as their vibrational dynamics. Accessing this information should be a critical step towards a better understanding of the energetics and the kinetics of interfacial processes, especially in electrochemical interfaces, where adsorption is always a competitive process between the ionic species and the solvent dipoles, which is controlled by the electrode potential.

The development of optical non-linear techniques benefits directly from the progress of the laser technology. In this respect, the Free electron laser offers a great advantage of producing a high power pulsed beam, tunable within a wide IR spectral range, allowing the simultaneous probe of several vibrational modes of the adsorbate. Combining the unique properties of the FEL with the high sensitivity and interface selectivity of SFG between centro-symmetric media allows the investigation of the vibrational properties of adsorbate species, with no interference from a signal of bulk species, which is forbidden in the electric dipole approximation. The recent experimental examples discussed in this lecture show clearly the advantage of this technique. The use of SFG, as well as various related second order optical processes, is increasing rapidly in various surface and interface research fields such as catalysis, corrosion, electrocatalysis, thanks to its versatility, its capability to probe any interface.